A numerical method for delayed partial differential equations describing infectious diseases

In this paper, we propose a numerical method for delayed partial differential equations that describe the dynamics of viral infections such as the human immunodeficiency virus (HIV) and the hepatitis B virus (HBV). We first prove that the proposed numerical method preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. By constructing appropriate discrete Lyapunov functionals, we show that the proposed method also preserves the global stability of equilibria of the corresponding continuous system with no restriction on the space and time step sizes. Moreover, the discrete model and main results presented in Qin et al. (2014) are extended and generalized.